How would you value 1,000 shares of company X?
I repeatedly claim that accounting is important, but I wanted to provide a simple example where current accounting practices may not be the best. GAAP rules state that for assets with an active market, quoted prices should be used for valuation. Here I have provided a hypothetical price distribution (it’s a Gaussian with sigma-squared equal to 0.1, mu equal to 4, truncated at 3 and 5) for a stock. Let’s say this represents the last month of trading for the stock. The distribution is clearly centered at 4. If this was any other distribution problem, you might say “4, plus or minus 1, with 99.8% confidence.” But, if the last trade occurred at a price of $4.235, GAAP rules state to value your stock holdings at $4.235. That’s roughly a 6% swing in valuation because of what may be considered a relatively low-probability trade.
The market today had a 1.2% swing in less than 2 hours. Today was substantially less volatile than other trading days in the past week. The accounting principle of “fair value” is the value one would receive by selling an asset to a buyer where neither party is under duress and both parties are knowledgeable. Yet if the price on a balanced mix of stocks changes 1% in a couple hours in one of the most active and liquid markets, how much certainty can be applied to the valuation of other assets?
Going back to this hypothetical scenario, what if a single trade occurred after market at $5? You might think it a bit dishonest for someone to value their shares at $5 when the closing price was $4.235. If they tried to sell their shares, there’s very little chance they’d get $5 at that point. After all, the last price is just that, the last price someone was willing to pay. It isn’t necessarily a great predictor of the next price someone is willing to pay. There’s a degree of uncertainty in valuation, something that isn’t reflected in GAAP.
The problem is even more complicated by the fact that I have presented the stock price distribution as Gaussian. Prices do not follow a normal distribution. Prices can move dramatically in a small time. As a consequence, even the “4, plus or minus 1, with 99.8% confidence” is incorrect, as it assumes a Gaussian distribution. Just because the hypothetical price has so far displayed a Gaussian distribution is no guarantee that the price will continue to follow such a distribution. In fact, the assumption that there exists normal distributions in prices is one of the model failures that contributed to the current crisis. Still, I think that at least the acknowledgement of uncertainty is a big step forward from representing value as a single number.
This is probably the simplest example I could come up with. Now consider the billions of dollars that companies assess themselves for things like “goodwill.” Changes in valuation rules make quarter-to-quarter comparisons of the same company and apples-to-oranges affair. Even without standards changes, companies can apply different accounting rules from one quarter to the next, as Apple did for last quarter’s results. Good companies announce such changes ahead of time, and provide additional data for analysts to make better apples-to-apples comparisons (pun mildly intended). Apple is again an example, providing a 1-year advance notice of the accounting change.
